Efficient Aerodynamic Shape Optimization of the Hypersonic Lifting Body Based on Free Form Deformation Technique

Abstract

Aerodynamic shape optimization (ASO) of hypersonic lifting body has become a significant research topic due to its significant performance advantages. As a universal parameterization, the free form deformation (FFD) technique has benefits including geometric independence, random deformation, and mesh synchronization. In this paper, an effective design method to apply the FFD technique in the ASO of a hypersonic lifting body is presented. Some commonly used basis functions are researched in FFD modeling of the windward side of a typical lifting body, including the Bernstein polynomial, the B-spline function, and the non-uniform rational B-spline (NURBS) function. An efficient aerodynamic simulation method combining Euler equations (non-viscous component) and skin friction drag (viscous component based on the compressible turbulence model) is then developed to minimize computational requirements. The accuracy of the proposed method is validated, and a significant decrease in processing time is observed. In addition, a kriging surrogate model combined with infilling sampling expected improvement (EI) criterion is developed to improve optimization efficiency. To obtain a lifting body with high lift-to-drag ratio that satisfies inner loading constraint, a baseline is optimized by manipulating its shape using the NURBS-based FFD technique. The results show that the optimal shape displays outstanding aerodynamic performance, and the effective design method can provide practical support for ASO of the hypersonic lifting body.

The Design of Cavity Resonators and Microwave Filters Applying Shape Deformation Techniques

“…Several other methods were developed later, including FFD based on nonuniform rational B-splines (NURBS) [11], [12]. Recently, shape deformation has been introduced into computational simulations of fluid dynamics [13]- [15] and low-frequency electromagnetics [16]. Some attempts to shape optimization using, e.g., level-set and topology gradient methods and Bézier curve parametrization have been reported for the design of microwave components, [17]- [20] but as far as we know, no attempts have yet been made to use shape deformation techniques to model complex 3D microwave structures.…”

An approach of Proper Orthogonal Decomposition-aided Free-form Deformation with application in compressor blade design

“…As FFD method dictates, the deformation relationship between the geometric model to be deformed and the control point positions is established. 43,19 This paper selects B-spline as the basis function in FFD modelling. In this paper, a rectangular lay-out with 6, 4, and three control points of 8m × 6m × 5m is constructed (c.f.…”

“…[15][16][17] To fix this problem, Free-form Deformation (FFD) has been deployed to characterize the three-dimensional, continuous change of arbitrary geometry and surrounding space, thereby providing wide design space. 18,19 The displacement of each control point that contributes the shape deformation were naturally the design variables. [20][21][22] Variations of FFD approaches include B-spline-based FFD, 23,24 grid-based FFD, 12,21 CAD-based FFD, 25,26 etc.…”

Point2FFD: Learning Shape Representations of Simulation-Ready 3D Models for Engineering Design Optimization

“…Depending on the amount of deformation and configuration of the lattice, FFD preserves the quality of the embedded mesh within reasonable tolerance and, thus, the quality of the simulation results [30,11,17]. Many works explore FFD and variations of the technique in design optimization problems, particularly in the context of aerodynamic applications using CFD [29,30,31,41,22,47]. However, FFD still requires human expertise to set up the lattice and select the degrees of freedom, which is challenging for unexperienced designers.…”